Find all positive integers x for which it’s possible….(see photo)

Given:-
[tex](2x+3),(3x+8),(6x+7)[/tex]To find:-
The possible value of x.
The property of triangle is sum of two sides of the triangle is greater than the other sides. so we get,
[tex]\begin{gathered} 2x+3+3x+8>6x+7 \\ 5x+11>6x+7 \\ 11-7>6x-5x \\ 4>x \end{gathered}[/tex]So the positive values are,
[tex]1,2,3[/tex]